# Sh:674

- Balogh, Z. T., Davis, S. W., Just, W., Shelah, S., & Szeptycki, P. J. (2000).
*Strongly almost disjoint sets and weakly uniform bases*. Trans. Amer. Math. Soc.,**352**(11), 4971–4987. arXiv: math/9803167 DOI: 10.1090/S0002-9947-00-02599-X MR: 1707497 -
Abstract:

A combinatorial principle CECA is formulated and its equivalence with GCH+ certain weakenings of \Box_\lambda for singular \lambda is proved. CECA is used to show that certain “almost point-< \tau” families can be refined to point-< \tau families by removing a small set from each member of the family. This theorem in turn is used to show the consistency of “every first countable T_1-space with a weakly uniform base has a point-countable base.” - published version (17p)

Bib entry

@article{Sh:674, author = {Balogh, Zoltan Tibor and Davis, Sheldon W. and Just, Winfried and Shelah, Saharon and Szeptycki, Paul J.}, title = {{Strongly almost disjoint sets and weakly uniform bases}}, journal = {Trans. Amer. Math. Soc.}, fjournal = {Transactions of the American Mathematical Society}, volume = {352}, number = {11}, year = {2000}, pages = {4971--4987}, issn = {0002-9947}, doi = {10.1090/S0002-9947-00-02599-X}, mrclass = {03E05 (03E35 03E75 54D70)}, mrnumber = {1707497}, mrreviewer = {Klaas Pieter Hart}, doi = {10.1090/S0002-9947-00-02599-X}, note = {\href{https://arxiv.org/abs/math/9803167}{arXiv: math/9803167}}, arxiv_number = {math/9803167} }